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Let \(f:\R→\R\) be a function defined by
\(f(x) = \begin{cases} x^2\sin(\frac{\pi}{x^2}), & \text{if } x \ne 0, \\ 0, & \text{if } x = 0. \end{cases}\)
Then which of the following statements is TRUE ?
Let \(f:\R→\R\) be a function defined by
\(f(x) = \begin{cases} x^2\sin(\frac{\pi}{x^2}), & \text{if } x \ne 0, \\ 0, & \text{if } x = 0. \end{cases}\)
Then which of the following statements is TRUE ?
\(f(x) = \begin{cases} x^2\sin(\frac{\pi}{x^2}), & \text{if } x \ne 0, \\ 0, & \text{if } x = 0. \end{cases}\)
Then which of the following statements is TRUE ?
Updated On: Jun 10, 2024
- f(x) = 0 has infinitely many solutions in the interval \([\frac{1}{10^{10}},\infin)\)
- f(x) = 0 has no solutions in the interval \([\frac{1}{\pi},\infin).\)
- The set of solutions of f(x) = 0 in the interval \((0,\frac{1}{10^{10}})\) is finite.
- f(x) = 0 has more than 25 solutions in the interval \((\frac{1}{\pi^2},\frac{1}{\pi})\)
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The Correct Option is D
Solution and Explanation
The correct option is (D):f(x) = 0 has more than 25 solutions in the interval \((\frac{1}{\pi^2},\frac{1}{\pi})\).
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